Since $G$ is a finite abelian group, we can write it as a direct sum of cyclic groups: $G \cong \mathbb{Z}_{p_1^{e_1}} \oplus \mathbb{Z}_{p_2^{e_2}} \oplus \cdots \oplus \mathbb{Z}_{p_n^{e_n}}$, where $p_i$ are prime numbers and $e_i$ are positive integers.
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